model of a new joint thread for a drilling tool and its ... · clearance was enlarged, which can...

Mech. Sci., 7, 189–200, 2016www.mech-sci.net/7/189/2016/doi:10.5194/ms-7-189-2016© Author(s) 2016. CC Attribution 3.0 License.

Model of a new joint thread for a drilling tool and itsstress analysis used in a slim borehole

Yu Wang1,2, Bairu Xia1,2, Zhiqiao Wang1,2, and Chong Chai1,2

1School of Engineering and Technology, China University of Geosciences, 100083 Beijing, China2Key Laboratory on Deep Geo-Drilling Technology of the Ministry of Land and Resources, China University

of Geosciences, 100083 Beijing, China

Correspondence to: Zhiqiao Wang ([email protected])

Received: 3 April 2016 – Revised: 16 June 2016 – Accepted: 6 July 2016 – Published: 31 August 2016

Abstract. The drilling pipe used in slim-borehole drilling performs well due to its low cost and high efficiency.Good sealing properties and coupling strength are the two keys to ensure that the pipe works correctly. In thispaper, a 68 mm diameter drilling pipe and its joint are developed. On the basis of Lame’s theory, the contactmodel of the joint thread is represented under different axial force, makeup torque, and pressure differencebetween inner and outer pipe. This model provides a good reference for judging the quality of sealing of thejoint thread. The analysis software ANSYS\Workbench is applied to stimulate the distribution of contact stressand sealing properties. A premium condition for drilling has been proposed, which provides a good theoreticalbasis for slim-borehole drilling.

1 Introduction

The drilling pipe used in slim-borehole drilling performswell due to its lower cost and higher efficiency (Zhang etal., 2015). Due to it being the most fragile component ofthe whole driving pipe string (Zhou, 2009), the joint threadhas attracted many researchers’ interest to improve its seal-ing quality (Li et al., 2014) and connection stress, which arethe key characteristics and areas of research emphasis withregard to the drilling pipe (Gong, 1995).

Many studies have been conducted on the joint threadaccording to American Petroleum Institute (API) stan-dards (American Petroleum Institute, 1995). Tafreshi andDover (1993) analysed threaded connections using a finite-element method (FEM) to find the greatest concentration ofstress under the action of axial loading. However, the contactstress was not reported. They optimized the shape of the teethof the threaded connection according to the load distribu-tion. Baryshnikov and Baragetti (2001) determined the loadbearing percentage of each tooth to calculate allowable loadsfor API drill string threaded connections under conditions ofbending and axial and combined loading. Griffin et al. (2004)analysed the stresses in a specific drill pipe connection un-der axial loading via FEM. Shahani and Sharifi (2009) built

a model contact between mating surfaces of the threads andanalysed this by using ABAQUS 6.6 standard code. The con-tact pressure on the contact surfaces and the effect of preloadon the stress concentration factor and were investigated. San-tus et al. (2009) compared the torsional strength between twoassembling techniques for connection of an aluminium drillpipe to a steel tool joint. Zhang et al. (2010) studied the ta-per trapezium joint threads of a drilling rod with a large hole.An improvement scheme for dual taper and cylinder seal hasbeen proposed which has successfully tackled the problemof stress concentration. A double-sealing shoulder was usedby Li et al. (2011) to develop a 73 mm diameter directlyconnected drill pipe without friction welding. The angularclearance was enlarged, which can satisfy the logging tooland drill-out tool. Zhu et al. (2013) established a drill pipethread FEM to aid failure analysis and to study solutions ina horizontal-direction drilling project. An XT-M joint devel-oped by Grant Prideco has reached a high level of technol-ogy. Its torsional capability is 70 % higher than the API’s,whose joint airtight capacity can reach 15 000 psi (Zhuang etal., 2015).

Published by Copernicus Publications.

190 Y. Wang et al.: Model of a new joint thread for a drilling tool and its stress analysis used in a slim borehole

Figure 1. Structure of the drilling pipe.

The contact model of the drill pipe has been analysed, anddifferent specifications of the thread have been designed, butthese connections are used in a large-sized oil well. Few stud-ies have been conducted with regard to modelling the corre-lation between the contact stress and tightness. At present,most of the drill pipes which are widely used in API standardare more than 89 mm in diameter (Shi et al., 2014; Wang etal., 2010). API seldom performs research on small-diameterdrill pipes, as these are unable to meet the requirements ofslim-borehole drilling.

In this paper, a 68 mm diameter drilling pipe and its jointare developed. On the basis of Lame’s theory, we create acontact model of the joint thread under different axial force,makeup torque, and pressure difference between inner andouter pipe, which provides a good reference for judgingthe quality of sealing of the joint thread. The analysis soft-ware ANSYS\Workbench is applied to stimulate the distri-bution of contact stress and sealing. A premium condition fordrilling has been proposed, which provides a good theoreticalbasis for slim-borehole drilling.

2 Model of the tool joint

2.1 Structure of the drilling pipe

Based on the requirements of a slim-borehole drill, the drillpipe is designed as shown in Fig. 1. The drill pipe consistsof pin joint 3, box joint 1 and drilling pipe body 2. The joint

Figure 2. Basic model of the joint for stress analysis.

is connected to the pipe body by friction welding. The jointsare connected to the pipe body by friction welding and stress-relieving annealing. The concentricity between the joints andpipe body is no greater than 0.4 mm. There is a flat surfaceinside and outside the welding position, whose faults areeliminated. The connector is the cone threaded joint, witha 1 : 30 thread taper and equilateral trapezoid thread. Theoverall quenching hardness can be equal to the hardness ofHRC30-35. The sealing cone concentricity of the respectiveinternal and external threads is no greater than 0.02 mm. Theend portion of the incomplete thread is cut off.

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Y. Wang et al.: Model of a new joint thread for a drilling tool and its stress analysis used in a slim borehole 191

Figure 3. Force diagram of thread A.

2.2 Theoretical foundation and assumptions

The thread is the most fragile but important component in thepipe. According to the theory of thread sealing, the thread’ssealing is realized through the interference fit between thethread’s teeth. The sealing quality is mainly influenced bythe stress of the connection of the joint thread, which hasa close relationship between axial load, makeup torque, andthe pressure difference between inner and outer pipe.

The projection of the drill pipe joints at one certain pointin the radial direction is a thick-walled cylinder. Based onthe analysis method of Lame’s stress, as shown in Fig. 2, theradial stress and circumferential stress of some certain pointunder mud pressure within the drill pipe are expressed asσr =

R21 ·Pi

R22 −R

21·

(1−

R22R2

)

σt =R2

1 ·Pi

R22 −R

21·

(1+

R22R2

) . (1)

Likewise, the radial stress and circumferential stress underthe mud pressure outside the drill pipe areσr =

R22 ·Pe

R22 −R

21·

(1−

R21R2

)

σt =R2

2 ·Pe

R22 −R

21·

(1+

R21R2

) . (2)

According to Lame’s theory, the radial displacement at anypoint with a radius of R can be expressed as

u=1−µE·R(R2

1Pi−R22Pe

)R2

2 −R21

+1+µE·R2

1R22 (Pi−Pe)

R(R2

2 −R21) . (3)

2.3 Contact mechanical model

2.3.1 Makeup torque influenced by the axial force

A drilling string formed by a pipe connection will be influ-enced by different axial forces when in use – for example,gravity, drilling pressure, and friction between the pipe and

the borehole wall. The force diagram of the screw thread isshown in Fig. 3. Thread A, intercepted from the box con-nector, is selected to make a mechanical analysis. Due to thespiral structure, the axial force will be decomposed, resultingin the box connector thread being subjected to, for example,the action of tangential forces and friction of the threadedsurface.

Force analysis on a section of box thread A, and accordingto the balance of force conditions, can be expressed as{f = µ ·N = µ · (Ff sinβ +Fb cosβ)Ff cosβ +Fb sinβ = f . (4)

To finish the above formulas, the tangential force Ff can beobtained because of the axial force,

Ff =µcosβ + sinβcosβ −µsinβ

·Fb =K ·Fb. (5)

From the analysis of Eq. (5), we can see that the axial forceof the threads has a direct impact on the makeup torque, andthere is a linear correspondence between them. The connec-tor thread’s contact surface’s friction coefficient is about 0.08and the thread angle is 3◦, which allows the contact surfaceto produce self-locking, and there will be no relative slidedue to the axial tension for the drill pile. The effect that axialforce produces is similar to the effect of makeup torque; theanalysis of the thread contact force under the action of axialforce can be converted to the analysis of makeup torque, andsubsequent analysis of torque contains the influence factorsof axial force.

2.3.2 Contact mechanical model of the joint

The drill pipe thread is a taper thread, and the inner radiusof the box joint is smaller than the outer radius of the pipebody for the radial joints at a certain point (such as toler-ance or machining error), and the surface contact pressure isgenerated at the contact interface. A schematic diagram ofthe connection between the box and the pin joint is shown inFig. 4.

Let Ra be the inner diameter of a pin joint, Rb the outsidediameter of a pin joint (which is also the inner diameter ofa box joint), and Rc the outside diameter of a box joint, andthe external pressure can be described as Pe= 0. Accordingto Eq. (3), the radial displacement of the inner surface of thebox connector is expressed as

u1 =Rb ·Pb

E·

(R2b +R

2c

R2c −R

2b +µ

). (6)

According to Eq. (3), the inner drilling mud pressure Pi= 0,and the radial displacement of the outer surface of the jointis

u2 =Rb ·Pb

E·

(R2a +R

2b

R2a −R

2b

+µ

). (7)

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Figure 4. Connection diagram of the box and the pin joint.

Because the increment of the inner diameter of the joint andthe reduction of the outer diameter of the joint is equal to theoriginal tolerance value, the existing constraint is

u1+ u2 = δ. (8)

By combining Eqs. (6)–(8), the surface contact pressure be-tween the pin and the box joint can be obtained by simplify-ing:

Pb =Eδ(R2b −R

2a

)(R2c −R

2b

)2R3

b

(R2c −R

2a

) . (9)

2.3.3 The circumferential stress model of joint

When fastening the screw, radial contact pressure is gener-ated in external threads. From Eq. (2), the maximum axialstress occurred in the inner wall, and according to Lame’stheory, the axial force and the circumferential stress gen-erated by fastening the pin joint external thread can be ex-pressed asR1 = RaR2 = Rb

σt1·max =−R2b ·Pb

R2b −R

2a

(1+

R2a

R2a

)=

2R2b ·Pb

R2b −R

2a

.

(10)

A negative sign of the circumferential stress is compressivestress. For the box joint, contact pressure is uniform internalstress. From Eq. (1), the maximum circumferential stress ison the inner wall; according to Lame’s theory, the axial forceand the circumferential stress generated by fastening the boxjoint internal thread can be expressed asR1 = RaR2 = Rb

σt2·max =−R2b ·Pb

R2c −R

2b

(1+

R2c

R2b

)=R2c +R

2b

R2b −R

2a

·Pb

. (11)

By inserting Eq. (9) into Eq. (11), the circumferential stressgenerated in the box joint internal thread can be obtained:

σt2max =Eδ(R2b −R

2a

)(R2b +R

2c

)2R3

b

(R2c −R

2a

) . (12)

In the above formula, σt2 is the axial stress of the thread onthe box joint that is produced (Pa).

When the drill pipe is subjected to the pressure of the in-ternal mud pressure Pi, the combined body of the pin jointand the box joint is subjected to the outward expansionforce, thereby causing the circumferential stress. Accordingto Lame’s theory, using the circumferential stress on the outersurface of the joint and the circumferential stress on the in-ner surface of the box joint to individually calculate the sur-face contact pressure Pc, which is caused by internal pres-sure between box joint and a pin joint mating surface, thecorresponding force is equal in magnitude and opposite indirection; thusσt i =

R2a ·Pi

R2c −R

2a

(1+

R2c

R2b

)

σte =R2b ·Pc

R2c −R

2b

(1+

R2c

R2b

)σt i = σte

. (13)

To complete Eq. (13), the contact pressure can be obtainedunder the action of mud pressure in the drill pipe,

Pc =R2a

R2b

·R2b −R

2c

R2c −R

2a

·Pi. (14)

2.4 Model and criterion of the sealing joint

The circumferential stress obtained from the above analysisis superimposed; it is expressed as tensile stress when theoutcome is positive. The following conditions must be satis-fied in order to avoid leaking from drill pipe joints. Firstly, arational stress distribution must be on the joints, which meansthat the sum of the axial force, makeup torque, and the con-tact pressure caused by the difference between the mud inthe inner and outer pipe must be larger than the differencebetween the inner and outer pipe. Secondly, the stress distri-bution must be kept balanced to ensure a larger sealing area.Therefore, the relationship can be expressed as

Pb+Pc ≥ |Pi−Pe|. (15)

3 Finite-element analysis

3.1 Material properties of joints

Material properties given in Table 1 are linear and isotropicas modal analysis ignores nonlinearities. Young’s modulusand density for a modal analysis must be specified.



Table 1. Material properties.

Component Materials Young’s Poisson’s Tensile Yield Hardnessmodulus ratio strength strength (HB)

(N mm−2) (MPa) (MPa)

Box joint 42CrMo4 205 000 0.3 1080 930 217Pin joint 42CrMo4 205 000 0.3 1080 930 217

Figure 5. Finite-element model (L – left shoulder; M – middle screw; R – right shoulder).

3.2 Finite-element modelling

A parametric 3-D model can be a better choice to compre-hensively reflect the situation of the joint. Considering thesmaller thread’s lead angle and that the main research em-phasis of this paper focuses on the relationship of the heli-cal tooth’s strain and the sealing quality, the influence of thethread’s lead angle can be ignored when modelling, whichmakes it possible to establish a 2-D model to simulate thejoint.

In this paper, the contact interference is applied to simu-late the makeup state. Friction torque of each tooth bucklecan be obtained through multiplying the contact pressure onthe interference surface by the distance between the contactsurface and the pipe centre. The equivalent makeup torquecan be obtained by integrating all the friction torques of thebuckle on the teeth. The value of the tooth interference ofthreads can be calculated on the basis of the number of turnson the buckle, as well as thread taper, pitch, tooth type angleand other parameters. Based on the API’s common methodof calculating the radial movement δr, the pin buckle to boxbuckle can be expressed as follows:

δr = 0.5T ×1L= 0.5T · n ·P = 0.5T ×θ

360×P. (16)

3.3 Element selection and meshing

Solid structural steel defined as 42CrMo4 is used for mod-elling of different components, i.e. the box joint, pin boxand drilling pipe body. For both the box joint and pin box,

Table 2. Interferences of contact surfaces.

Addendum Bearing Guide Shouldersurface surface surface

Interference (mm) 0.0100 0.0025 0.0025 0.6000

“manual contact region” contact elements are used; there-fore, both of the threaded surfaces are of the same elementtype. Two-dimensional “manual contact region” contact el-ements, in combination with the command CONTACT forpin joint surface and TARGET for the box joint surface areused between the box joint and pin joint surface to simulatecontact distribution.

Body-sizing meshing is used throughout in the regions ofthe high-stress distribution box, i.e. box joint faces and pinjoint faces. Front areas of the model are meshed first and thenthe same meshing pattern of meshed area is swept over thevolumes. The command “Refinement” is used for the mesh-ing with 3× amplification. The FEM of the joint thread fit-ting is shown in Fig. 5.

3.4 Boundary conditions and loading

In order to eliminate the boundary effect in simulation, thepipe length in the model should be 2 times longer than thelength of the drill pipe end to the thread disappearing point.The equivalent torque and axial force are applied by settingthe contact interference or applying a preload.



δns = δr · cosαδnl = δr · sin14.5◦

δnd = δr · sin14.5◦−1(17)

Through the above formulas, the amount of interference ofthe thread of each surface can be calculated by setting theoffset to define the size of the contact between the unit andthe target unit in ANSYS in a real constant offset, which isthe value of the force. Using the software, the axial tensionand internal pressure can be simulated in the form of uni-form force, which can be loaded directly onto the threadedmodel. In the three different mating connector states, includ-ing finger-tight, tight state machine and state interference, thetension and the pressure of 0–300 kN are respectively loadedonto a pair of mating threaded joints per 50 kN. The stressdistribution and air tightness are studied according to the pre-ceding model.

The 68 mm diameter drill pipe is mainly used in the wellwith the maximum depth of 2000–2500 m. The maximumaxial tension and compression load is calculated at about300 kN on account of its weight and length of the l strings,which are selected as the parameters used. In addition, thedata are collected with a gradient of 50 kN to better reflectstress.

4 Results and analysis

4.1 Pipe joints and its connection states

There are 12 screw threads on the joint. Three different ba-sic states will exist during tightening of the pipe joints. Asshown in Fig. 6, for connection state A, the makeup torqueis relatively small, resulting in a certain gap existing in thethread shoulder. In connection state B, the thread shouldersare in contact with each other but with no pressure generated.In connection state C, the thread should also be in contactand the pressure can be very large. The three different statescan represent three different practical situations to describethe joint’s strength and tightness.

4.2 Stress distribution of pipe joints

Tensile force will be exerted on the pipe while dealing withproblems, while pressure will be exerted on the pipe duringdrilling. Based on experience with simulation and real prac-tice, for the pipe 68 mm diameter, the maximum tensile stressis 250 kN, and the maximum pressure is 150 kN. Therefore,there are corresponding changes under three different con-nection states, with the force changes in the range of 150–250 kN. The selection of a pipe can be determined on thebasis of the changes.

4.2.1 Joint state under allowable tensile force

When the axial tension reaches 250 kN in the joint’s finger-tight connection state, the maximum contact stress of the

(a)

(b)

(c)

Figure 6. Connection states of the joints.

thread reaches 11.43 MPa. The left sealing surface contactstress reaches 397.24 MPa when the drill machine is in a statethat is tight but under interference. The left sealing surfacecontact stress reaches 397.24 MPa when the drill machine isin an interference state. In Fig. 7, it is shown that, with theincrease in torque on the buckle, contact stress between thepin and the box connectors will correspondingly increase.

4.2.2 Joint state under allowable yield force

When axial tension reaches 150 kN in the joint’s finger-tightconnection state, as shown in Fig. 8, the maximum contactstress of the thread reaches 6.13 MPa. The left sealing sur-face contact stress reaches 488.6 MPa when the drill machineis in a state that is tight but under interference. The left seal-ing surface contact stress reaches 931.6 MPa when the drillmachine is in an interference state. Similarly, it is shown that,with the increase in torque on the buckle, contact stress be-tween the pin and the box connectors will also correspond-ingly increase.

4.2.3 Stress change principle with three differentconnection types

As shown in Fig. 9, in comparison with the influence ax-ial load, the influence of the connection type is more ob-vious. This shows that the makeup torque is the key factorthat determines the sealing quality and joint strength. Whenthe thread is in a finger-tight state, the thread engagement isunstable, especially when tensile force is exerted. When themachine changes gradually to the interference state from thetight state, the contact stress is larger on both ends of theshoulder but the contact stress in the middle of each thread isgenerally relatively stable.

When the drill bit is in connection modeA, too much strainwill generate on the thread, resulting in structural damage af-ter axial tension reaches 251 kN. When in mode B, the con-tact stress for each part of the joint is always within the stresslimits, but with the increase in the makeup torque, the con-tact stress of the sealing surface will further increase. Whenin mode C, and the stress exceeds 150 kN, the local stress



(a)

(c)

(e)

(b)

(d)

(f)

Figure 7. Joint stress and strain under allowable tensile force: (a) joint stress in state A, (b) joint strain in state A, (c) joint stress in state B,(d) joint strain in state B, (e) joint stress in state C and (f) joint strain in state C.

Figure 8. Joint stress and strain under allowable tension force: (a) joint stress in state A, (b) joint strain in state A, (c) joint stress in state B,(d) joint strain in state B, (e) joint stress in state C and (f) joint strain in state C.



0 1 2 3 4 5 6 7 8 9 10 11 120

1

2

3

4

5

6

7

Stre

ss /M

Pa

Number of screw threads

0 50 k N 100 k N 150 k N 200 k N 250 k N 300 k N

0 1 2 3 4 5 6 7 8 9 10 11 120

2

4

6

8

10

12

Stre

ss /M

Pa


0 50 k N 100 k N 150 k N 200 k N 250 k N

0 1 2 3 4 5 6 7 8 9 10 11 120

20

40

60

80

100

120

Stre

ss /M

Pa


0 50 k N 100 k N 150 k N 200 k N 250 k N 300 k N

0 1 2 3 4 5 6 7 8 9 10 11 120

20

40

60

80

100

120

140

160

Stre

ss /M

PaNumber of screw threads

0 50 k N 100 k N 150 k N 200 k N 250 k N 300 k N

0 1 2 3 4 5 6 7 8 9 10 11 120

100

200

300

400

500

600

Stre

ss /M

Pa


0 50 k N 100 k N 150 k N

0 1 2 3 4 5 6 7 8 9 10 11 120

100

200

300

400

500

600

Stre

ss /M

Pa


0 50 k N 100 k N 150 k N 200 k N 250 k N 300 k N

(a) (b)

(c) (d)

(e) (f)

Figure 9. Stress change principle with different connection types: (a) tension stress in state A, (b) tensile stress in state A, (c) tension stressin state B, (d) tensile stress in state B, (e) tension stress in state C and (f) tensile stress in state C.

will exceed the yield limit. The joints’ carrying capacity willdecrease during the loading process because the initial stressis too large, which causes the bearing capacity of the jointon the axial pressure to be less than the axial tension. At thesame time, the thread will produce plastic strain, affectingthe airtightness. In addition, the overall strength of the jointswill also decrease under the dynamic loading.

All in all, the interference fit between the threads signif-icantly increases the overall strength of the joint effect, butthe contact pressure is not always better. When taking thelimitations of the material itself into account, the followingcondition must be greater than the pressure difference insideand outside the drill pipe, which additionally should remainstable during operation.

4.3 Calculation of the premium makeup torque

The scale model

The law of thread stress changing in different axial loadingis found through the model simulation mentioned above. It isconcluded that we can apparently get more data through sim-ulation experiments through increasing the number of teeth.Some errors exist between the actual situation and the simu-lation. Therefore, the scale model shown in Fig. 10 is intro-duced again to calculate the makeup torque.

Model exposure settings, mesh, interference, etc. are setwith reference to the original model. The working environ-ment is fairly complex during drilling. A sudden increase intorque will probably occur if there is friction between thedrill pipe and the borehole wall or if faults occur. In thiscase, the up-torque is too large, which will result in the ini-tial contact stress exceeding the limit, causing plastic defor-



Figure 10. The scale model.

Figure 11. Connection state under optimum makeup torque: (a) stress under optimum makeup torque and (b) strain under optimum makeuptorque.

mation and affecting the joint’s airtightness. Therefore, thesafety coefficient should be introduced to provide a safe elas-tic stress range. In order to get the best deduction, the refer-ence value for the maximum contact stress safety factor isgiven as 620 MPa, whereby the amount of thread interfer-ence can be drawn in the radial direction. Interferences of thecontact surfaces are shown in Table 2. The values of interfer-ences of the axial and the bearing surfaces can be calculatedthrough the radial values. Therefore, we can get the distribu-tion of the stress and strain under optimum makeup torque,which are shown in Fig. 11. We can see the stress distributionhas more uniform than aforementioned states, and it must bekept balanced to ensure a larger sealing area.

The stress distribution is mostly influenced by torque,which determines the stress magnitudes on different jointcontact surfaces, affecting the strength of the connection andsealing joints. The torque is obtained from the values of fric-tion force and centre distance in simulation, and it is accumu-lated from three different components: the shoulder, sealingsurface and screw thread. As shown in Table 3, the makeuptorque will reach 3320.66 N m−1 when in the premium state,where the torque between the buckle teeth is 2560.32 N m−1,and the torque between the sealing surface and the shoulder is760.34 N m−1. The torque in each case takes up 77 and 23 %of the overall makeup torque, respectively, which means that



Table 3. Composition of the optimum makeup torque.

Items Position Friction Centre Torque Totalforce distance (N m−1) torque(kN) (mm) (N m−1)

Left shoulder Contact surfaces 2.88 32.10 92.45492.40

Left sealing surface Contact surfaces 14.65 27.30 399.95

1st screw threadAddendum 5.68 29.50 167.56

469.97Dedendum 8.55 27.62 236.15Bearing surface 2.32 28.56 66.26

2nd screw threadAddendum 5.05 29.74 150.19


3rd screw threadAddendum 5.21 29.98 156.20


4th screw threadAddendum 5.18 30.22 156.54


5th screw threadAddendum 5.47 30.46 166.62


Right sealing surface Contact surfaces 2.79 30.70 85.65267.94

Left shoulder Contact surfaces 4.94 36.90 182.29

Total: 3320.66 Nm

it plays a significant role in keeping the sealing quality of thepipe.

5 Conclusions

1. The connection type – A, B, and C – has a greater ef-fect on the contact stress than the axial loading’s effect,which means the makeup torque is the key factor thatdetermines the joint’s strength and its sealing quality.

2. The joints’ double shoulders can significantly boost thethread’s overall stability because the shoulder reducesthe phenomenon of stress concentration and takes a partof axial force, which enhances the thread’s overall seal-ing quality and axial strength.

3. With the increase in the makeup torque, the maximumcontact stress gradually changes from the thread’s teethto the shoulders on both ends, which enhances the over-all sealing quality but weakens the structural strength.Plastic deformation occurs on some of the thread, whichexceeds the allowable load.

4. When the makeup torque reaches up to 3320.66 Nm, thecontact stress of the sealing shoulder is greater than thepressure difference between the inner and outer pipe.The even distribution of the joint thread’s stress con-tributes to the pipe joint’s sealing and overall strength,which provides a good reference for selecting the pa-rameters of the drilling tool’s makeup.



Appendix A

Table A1. Nomenclature.

σr radial stress, Paσt circumstantial stress, PaR1, R2 the inner and outer radius, respectively, mR radius at any point, mE elastic modulus, Paµ Poisson’s ratiou radial displacement when the radius is R, mPi drilling mud pressure from inner drilling pipe, PaPe drilling mud pressure from outer drilling pipe, Paf friction force produced by axial force, Nµ friction coefficient of screw threadN supporting force on screw thread face, NFf tangential force of the thread, NFb component force of drill pipe, Nβ helix angle, radK proportional coefficientu1 radial displacement of the inner surface of the box joint, mu2 radial displacement of the outer surface of the pin joint, mRa inner diameter of the pin joint, mRb outer diameter of the pin joint, mRc outer diameter of the box joint, mPb radial surface contact pressure between pin and box joints, Nσt1 axial stress of the thread on the pin joint produced, Paσt2 axial stress of the thread on the box joint produced, PaPc contact pressure produced by the inner drilling mud pressure, NPi mud pressure inside drill pipe, Nσt i circumferential stress in the inner surface of the box joint, Paσte circumferential stress in the outer surface of the pin joint, Paδr radial movement of the pin buckle to box buckle, mT thread taper1L axial movement of the pin buckle to box buckle, mn number of button turns on compact machineP thread pitch, mθ buckle rotation angle, radδns normal interference between addendum and dedendum, mδnl normal interference of the bearing surface, mδnd interference of the guide surface, m1 original gap of the guide surface, m



Competing interests. The authors declare that they have no con-flict of interest.

Acknowledgements. This work is supported by the Na-tional Natural Science Foundation of China (no. 41572360,11472249), the National Key Technology Support Program ofChina (no. 2015BAD20B02) and the Fundamental ResearchFunds for the Central Universities (no. 292015061). We thank theresearchers for their excellent work, which was of great help forour academic study.

Edited by: D. D. GanjiReviewed by: three anonymous referees

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model of a new joint thread for a drilling tool and its ... · clearance was enlarged, which can...

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